Subtopic: Steering and hydraulic control systems used in tractors
Question Statement:
A tractor is provided with an Ackerman steering gear mechanism. If b is the wheel base, c the distance between the front wheel pivot points, θ the steering angle of the inner wheel and φ the steering angle of the outer wheel, the fundamental relationship to be satisfied to avoid skidding of the two front wheels during a turn is given by
Options:
(A) tanφ − tanθ = c/b
(B) cotφ − cotθ = c/b
(C) tanθ − tanφ = b/c
(D) cotφ − cotθ = b/c
Official Answer Key:
B
Step-by-Step Solution & Explanation
For true rolling (no skid), both front wheels must trace concentric circles about the same instantaneous centre on the extended rear axle. Geometrically, for wheel-base b and pivot-point spacing c, this condition is the standard Ackermann relation cotφ − cotθ = c/b, where φ is the outer (smaller) steering angle and θ the inner (larger) steering angle. Answer: (B).
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